The Existence of Integers Less than p Belonging to ep&lt;sup&gt;r-1&lt;/sup&gt; (mod p&lt;sup&gt;r&lt;/sup&gt;)

Maxfield, John E.; Maxfield, Margaret W.

doi:10.2307/3029157

Cited by 3 publications

(4 citation statements)

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“…Elemental analyses were determined by Elemental Microanalysis, Ltd. (Okehampton, Devon, U.K.). 6-Mes, 7-Mes, 6-MesDAC, and CpNi(PPh 3 )Br were prepared according to literature procedures.…”

Section: Experimental Sectionsupporting

confidence: 91%

Influence of Ring-Expanded N-Heterocyclic Carbenes on the Structures of Half-Sandwich Ni(I) Complexes: An X-ray, Electron Paramagnetic Resonance (EPR), and Electron Nuclear Double Resonance (ENDOR) Study

et al. 2016

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Potassium graphite reduction of the half-sandwich Ni(II) ring-expanded diamino/diamidocarbene complexes CpNi(RE-NHC)Br gave the Ni(I) derivatives CpNi(RE-NHC) (where RE-NHC = 6-Mes (1), 7-Mes (2), 6-MesDAC (3)) in yields of 40%-50%. The electronic structures of paramagnetic 1-3 were investigated by CW X-/Q-band electron paramagnetic resonance (EPR) and Q-band H electron nuclear double resonance (ENDOR) spectroscopy. While small variations in the g-values were observed between the diaminocarbene complexes 1 and 2, pronounced changes in the g-values were detected between the almost isostructural species (1) and diamidocarbene species (3). These results highlight the sensitivity of the EPR g-tensor to changes in the electronic structure of the Ni(I) centers generated by incorporation of heteroatom substituents onto the backbone ring positions. Variable-temperature EPR analysis also revealed the presence of a second Ni(I) site in 3. The experimental g-values for these two Ni(I) sites detected by EPR in frozen solutions of 3 are consistent with resolution on the EPR time scale of the disordered components evident in the X-ray crystallographically determined structure and the corresponding density functional theory (DFT)-calculated g-tensor. Q-band H ENDOR measurements revealed a small amount of unpaired electron spin density on the Cp rings, consistent with the calculated SOMO of complexes 1-3. The magnitude of theH A values for 3 were also notably larger, compared to 1 and 2, again highlighting the influence of the diamidocarbene on the electronic properties of 3.

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“…Elemental analyses were determined by Elemental Microanalysis, Ltd. (Okehampton, Devon, U.K.). 6-Mes, 7-Mes, 6-MesDAC, and CpNi(PPh 3 )Br were prepared according to literature procedures.…”

Section: Experimental Sectionsupporting

confidence: 91%

Influence of Ring-Expanded N-Heterocyclic Carbenes on the Structures of Half-Sandwich Ni(I) Complexes: An X-ray, Electron Paramagnetic Resonance (EPR), and Electron Nuclear Double Resonance (ENDOR) Study

et al. 2016

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“…Maxfield [7,Theorem] proved that Lemma 4. Let p be an odd prime number and let r > 0 be a positive integer.…”

Section: Bray and Warren [1 Theorem 1] Proved Thatmentioning

confidence: 99%

“…Fortunately, it turns out from [6,5,7] that it is easy to prove that q 2 does not divide M p when p ≡ 3 (mod 4) is a Sophie Germain's prime. This proves also that there are no Wieferich's primes q = 2p + 1 where p ≡ 3 (mod 4) is a prime number.…”

Section: Introductionmentioning

confidence: 99%

On special Wieferich's primes

Gallardo

2010

Preprint

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“…The synthesis of the unsymmetrical Ni complexes of the type Ni(S2CNRz)PR>X, where R = Et or Me, R' = n-Bu or Ph, and X = C1, Br, or I, were first reported by Maxfield' in 1970. Subsequently, Fackler et al* and Cornock and Stephensong reported preparations of the Pd and Pt analogs.…”

Section: Mixed-ligand Diselen O Carbamatesmentioning

confidence: 99%